The subject application relates to printer color characterization systems and methods. While the systems and methods described herein relate to printer color characterization in computing systems and the like, it will be appreciated that the described techniques may find application in other color characterization systems or methods, printer calibration applications, and/or other printer color assessment and/or adjustment methods.
Color device characterization is a crucial task in color management. The characterization process essentially establishes a relationship between device dependent (e.g. printer CMYK) values, and device independent (e.g. CIELAB) values. Several color management tasks such as derivation of International color consortium (ICC) profiles, color transforms for calibration etc. benefit from an accurate mathematical characterization of the physical device. For color printers, characterization is an expensive process involving large number of patch measurements. Further, this process is halftone dependent (e.g., patch printing), where measuring and associated computation is scaled proportionally to the number of halftoning methods. Recent research has proposed methods for improving the accuracy of binary color printer models so that patch printing and measuring does not have to be repeated across halftones. For instance, a 4-color 2×2 printer model requires printing and measuring 16,576 binary color patches. However, such a large number of patches is tedious and computationally expensive.
Color printer characterization is the process of deriving a mathematical transform which relates printer CMY(K) to its corresponding device independent representation, e.g. spectral, CIELAB etc. The forward characterization transform defines the response of the device to a known input, thus describing the color characteristics of the device. The inverse characterization transform compensates for these characteristics and determines the input to the device that is required to obtain a desired response. For printers therefore, a CMY(K)→CIELAB mapping represents a forward characterization transform while the CIELAB→CMY(K) map is an inverse transform.
Full color characterization can be performed as needed to correct for temporal color drift or media color drift, as described, e.g., in R. Bala, “Device Characterization,” Digital Color Imaging Handbook, Chapter 5, CRC Press, 2003. This is a time consuming operation that is preferably avoided in most xerographic printing environments. Simpler color correction methods based on 1-dimensional (1-D) tone response curve (TRC) calibration for each of the individual color channels are usually sufficient and are easier to implement. The 1-D TRC calibration approach is also well-suited for use of in-line color measurement sensors, but is typically halftone dependent. In general, for each color channel C and for each halftone method H, a series of test patches are printed in response to N different digital input levels which requires C×H×N test patches, because the test patches must be printed for each halftone method. It has been found in practice that N must not be too small (e.g., N=16 is usually too small) because the TRC for each halftone method is typically not a smooth curve, due to dot overlapping and other microscopic geometries of the printer physical output. Existing methods for 1-D calibration, being halftone dependent, are measurement-intensive, and are not practical for in-line calibration, especially in print engines equipped with multiple halftone screens.
Previously, Wang and others have proposed a halftone independent printer model for calibrating black-and-white and color printers. This halftone independent printer model is referred to as the two-by-two (2×2) printer model and is described, e.g., in the following U.S. Patents, all of which are hereby expressly incorporated by reference into this specification: U.S. Pat. No. 5,469,267, U.S. Pat. No. 5,748,330, U.S. Pat. No. 5,854,882, U.S. Pat. No. 6,266,157 and U.S. Pat. No. 6,435,654. The 2×2 printer model is also described in the following document that is also hereby expressly incorporated by reference into this specification: S. Wang, “Two-by-Two Centering Printer Model with Yule-Nielsen Equation,” Proc. IS&T NIP14, 1998.
One technique to build a printer characterization transform involves printing and measuring a large set of color samples, i.e. CMY(K) patches, in conjunction with mathematical fitting and interpolation to derive CMY(K)→Lab mappings. The accuracy of the characterization transform depends on the number (N) of patches printed and measured. Crucially, note that these patches correspond to contone CMY digital values, i.e. their binary representation is halftone dependent. Hence, deriving characterization transforms for a printer equipped with M halftone screens, requires N*M patches. Even for modest choices of N, M, e.g. N=1000, M=4, this number quickly grows to be unmanageable. Note that N cannot be made very small without compromising accuracy under these conventional techniques. As multiple media are thrown into the mix, the number scales further with the number of distinct media employed, i.e. N×M×P patches are needed where P distinct media types are used.
A classical 2×2 printer model exhibits several features, including a that it is a halftone printer model at the pixel level. Different from most other printer models, which only estimate the average color appearance of an area with many pixels, the 2×2 printer model provides the color appearance of every output pixel. The output pixels are defined differently from the input pixels by a shifted coordinate, although the output pixels maintain the same size and the same shape of the inputs. The color appearance of each output pixel depends on the binary values of four input pixels located at four corners of the output. The 2×2 printer model is a measurement-based printer model. All N colors defined by the 2×2 printer model can be represented by N unique calibration halftone patches and can be printed and measured independently. The total number of independent 2×2 colors depends on the number of colorants. For a monochromatic printer, N=7; for a CMY, three-colorant printer, N=1072; and a CMYK, four-colorant printer, N=16,576.
One conventional approach to reducing color patches involves patch reduction via colorant decomposition. To reduce the number of patches in calibrating a three- or four-colorant printer, the full set of the 2×2 colors, specified by the total number N, may be derived by a rendering method from a selected subset of 2×2 colors. As described in Wang et al., a total of 488 2×2 patches, most in one and two colorants, representing the selected subset were printed by a CMYK four-colorant printer and measured in spectral reflectance. The complete set of independent 2×2 colors, 16,576 in total for the CMYK printer, was derived by a method described in the reference. Although patch reduction was achieved, the color accuracy of the derived full set of the 2×2 colors was inadequate.
Accordingly, there is an unmet need for systems and/or methods that reduce the number of binary patches required to achieving a desired model accuracy, while overcoming the aforementioned deficiencies.